Is there a Boolean data type in Microsoft SQL Server like there is in MySQL?

You may want to use the BIT data type, probably setting is as NOT NULL:

Quoting the MSDN article:

bit (Transact-SQL)

An integer data type that can take a value of 1, 0, or NULL.

The SQL Server Database Engine optimizes storage of bit columns. If there are 8 or less bit columns in a table, the columns are stored as 1 byte. If there are from 9 up to 16 bit columns, the columns are stored as 2 bytes, and so on.

The string values TRUE and FALSE can be converted to bit values: TRUE is converted to 1 and FALSE is converted to 0.

You could use the BIT datatype to represent boolean data. A BIT field's value is either 1, 0, or null.